Some dogs just don't like their feet touched-they don't have to hurt. And he might just be a lazy guy. If it were me, I'd bring him to the vet to just check-for us we don't have to pay office visit fees (we're at Banfield and pay a wellness fee every month). For most people the banfield plan probably wouldn't be beneficial, but for us, we're in there a lot (and I have no problem bringing my dogs in just in case).

Also, since he's so young and you have hard floors-it could just be that. I thought it was advised to have pups on softer ground when they were young-especially if you're worried about them "knuckling over". Obviously, you can't change the flooring in your house just like that...but maybe some throw rugs or something to give him better traction?

It's always better to be safe than sorry and it's always cheaper to address health issues sooner rather than later. It's too hard to tell from the video whether he's just confused and reluctant because he doesn't know what's going on but it looked to me like he has a short stride. When in doubt, get it checked out.